LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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◆ srzt02()

real function srzt02 ( integer  m,
integer  n,
real, dimension( lda, * )  af,
integer  lda,
real, dimension( * )  tau,
real, dimension( lwork )  work,
integer  lwork 
)

SRZT02

Purpose:
 SRZT02 returns
      || I - Q'*Q || / ( M * eps)
 where the matrix Q is defined by the Householder transformations
 generated by STZRZF.
Parameters
[in]M
          M is INTEGER
          The number of rows of the matrix AF.
[in]N
          N is INTEGER
          The number of columns of the matrix AF.
[in]AF
          AF is REAL array, dimension (LDA,N)
          The output of STZRZF.
[in]LDA
          LDA is INTEGER
          The leading dimension of the array AF.
[in]TAU
          TAU is REAL array, dimension (M)
          Details of the Householder transformations as returned by
          STZRZF.
[out]WORK
          WORK is REAL array, dimension (LWORK)
[in]LWORK
          LWORK is INTEGER
          length of WORK array. LWORK >= N*N+N*NB.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

Definition at line 89 of file srzt02.f.

91*
92* -- LAPACK test routine --
93* -- LAPACK is a software package provided by Univ. of Tennessee, --
94* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
95*
96* .. Scalar Arguments ..
97 INTEGER LDA, LWORK, M, N
98* ..
99* .. Array Arguments ..
100 REAL AF( LDA, * ), TAU( * ), WORK( LWORK )
101* ..
102*
103* =====================================================================
104*
105* .. Parameters ..
106 REAL ZERO, ONE
107 parameter( zero = 0.0e+0, one = 1.0e+0 )
108* ..
109* .. Local Scalars ..
110 INTEGER I, INFO
111* ..
112* .. Local Arrays ..
113 REAL RWORK( 1 )
114* ..
115* .. External Functions ..
116 REAL SLAMCH, SLANGE
117 EXTERNAL slamch, slange
118* ..
119* .. External Subroutines ..
120 EXTERNAL slaset, sormrz, xerbla
121* ..
122* .. Intrinsic Functions ..
123 INTRINSIC max, real
124* ..
125* .. Executable Statements ..
126*
127 srzt02 = zero
128*
129 IF( lwork.LT.n*n+n ) THEN
130 CALL xerbla( 'SRZT02', 7 )
131 RETURN
132 END IF
133*
134* Quick return if possible
135*
136 IF( m.LE.0 .OR. n.LE.0 )
137 $ RETURN
138*
139* Q := I
140*
141 CALL slaset( 'Full', n, n, zero, one, work, n )
142*
143* Q := P(1) * ... * P(m) * Q
144*
145 CALL sormrz( 'Left', 'No transpose', n, n, m, n-m, af, lda, tau,
146 $ work, n, work( n*n+1 ), lwork-n*n, info )
147*
148* Q := P(m) * ... * P(1) * Q
149*
150 CALL sormrz( 'Left', 'Transpose', n, n, m, n-m, af, lda, tau,
151 $ work, n, work( n*n+1 ), lwork-n*n, info )
152*
153* Q := Q - I
154*
155 DO 10 i = 1, n
156 work( ( i-1 )*n+i ) = work( ( i-1 )*n+i ) - one
157 10 CONTINUE
158*
159 srzt02 = slange( 'One-norm', n, n, work, n, rwork ) /
160 $ ( slamch( 'Epsilon' )*real( max( m, n ) ) )
161 RETURN
162*
163* End of SRZT02
164*
xerbla
subroutine xerbla(srname, info)
Definition cblat2.f:3285
slamch
real function slamch(cmach)
SLAMCH
Definition slamch.f:68
slange
real function slange(norm, m, n, a, lda, work)
SLANGE returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value ...
Definition slange.f:114
slaset
subroutine slaset(uplo, m, n, alpha, beta, a, lda)
SLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values.
Definition slaset.f:110
sormrz
subroutine sormrz(side, trans, m, n, k, l, a, lda, tau, c, ldc, work, lwork, info)
SORMRZ
Definition sormrz.f:187
srzt02
real function srzt02(m, n, af, lda, tau, work, lwork)
SRZT02
Definition srzt02.f:91
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